Current-controlled memristors: Resistive switching systems with negative capacitance and inverted hysteresis

Resistive switching in memristors is being amply investigated for different applications in nonvolatile memory, neuromorphic computing, and programmable logic devices. Memristors are conducting devices in which the conductance depends on one or more slow internal state variables, and they exhibit strongly nonlinear properties and intense memory effects. Here, we address the characterization of current-controlled memristors by small-perturbation frequency-resolved impedance techniques. We show that the equivalent circuit obtained at different stationary points provides essential information about the dynamic behavior in voltage cycling and transient response to a square perturbation. The general method enables the analysis of stability and hysteresis in current-voltage curves. The current-controlled memristor very naturally produces a negative capacitance effect, and we review several devices reported in the literature, including discharge tubes and metal-oxide memristors, to expose the deep connections between the sign of the capacitance and the type of hysteresis.

Figure 1

(a) Onset of the memristor from a low-resistance state to a high-resistance state at positive voltage requires inverted (counterclockwise, inductive) hysteresis. Reset to the low-resistance state at negative polarity shows regular (clockwise, capacitive) hysteresis. (b) Successive application of voltage-sweep cycles increases the conduction state, causing potentiation of the synapse by reaching states of higher conductivity.

Figure 2

Equivalent-circuit representation of the impedance of a chemical inductor (a) and a current-controlled memristor (b). Square resistance is $R_c=-R_b{C}_m{C}_a{\omega }^2$.

Figure 3

Impedance spectra of the model memristor for parameters $C_m=0.1$, $R_b=3$, for two cases: (a) $R_a=1,C_a=10$, (b) $R_a=-1,C_a=-10$. Cyan point is the resistance at zero frequency, $R_{\text{dc}}$, and the dashed line arc is the parallel combination, $R_{\text{dc}}{C}_m$.

Figure 4

(a) Schematic of the ${\mathrm{TiO}}_2$ memristor device and four-wire time-sampled current-voltage test setup used for the state-test protocol. w and $R_s$ represent the tunneling barrier width and electroformed channel resistance, respectively. (b) Example of a switching $I\text{−}V$ curve. Positive polarity turns the device off, while negative polarity turns the device on. Blue curve corresponds to the fit for a conducting-channel series resistance of R_s = (215 ± 6) D. Reproduced with permission from Ref. [82]. Copyright 2009 American Institute of Physics.

Figure 5

Current-voltage characteristic for a fluorine-doped tin oxide (FTO)/poly(3,4-ethylenedioxythiophene) (PEDOT):polystyrene sulfonate (PSS)/MAPbI₃/2,2${}^{\mathrm{\prime }}$,7,7${}^{\mathrm{\prime }}$-Tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9${}^{\mathrm{\prime }}$-spirobifluorene (Spiro-MeOTAD)/$\mathrm{Au}$ memristor device at a scan velocity of 0.5 V/s. Reproduced with permission from Ref. [83]. Licensed under a Creative Commons Attribution (CC BY 4.0) license.

Figure 6

(a) Current-density–voltage characteristic of a FTO/PEDOT:PSS/MAPbI₃/$\mathrm{Au}$ memristor measured from 0 to 100 mW/cm² using a blue-light source (470 nm) and 0.1-cm² active area. (b) Magnified view of the scale. (c) Low-frequency capacitance enhancement with illumination intensity. Reproduced with permission from Ref. [85]. Licensed under a Creative Commons Attribution (CC BY 4.0) license.

Figure 7

Current-voltage curves at constant voltage sweep of velocity, $v_s$, starting at equilibrium, $I_{ss}(u_0)$ (gray line, orange point), from $u_0=0.1$ to $u_1=1.4$. $d=0.5,V_T=0.5;I_s=1;a=1,b=1,{\tau }_k=0.01,R_b=0.5,R_s=0,C_m=0$.

Figure 8

(a) Transient charging current for the linear memristor model for a square voltage pulse, $V_{\text{app}}=1.5$, of duration $\mathrm{\Delta }t$. $d=0.5,V_T=0.5;I_s=1;a=1,b=1,{\tau }_k=0.01,R_b=0.5,R_s=0.1,C_m=1$. Gray line is $\mathrm{\Delta }I=V_{\text{app}}/R_s$, green line is $V_{\text{app}}/(R_s+R_b)$, and purple line is $I_{\text{dc}}(V_{\text{app}})$. (b) Evolution of the internal voltage. Gray line is $V_{\text{app}}$.

Figure 9

Current-voltage curves at constant voltage sweep of velocity, $v_s$, starting at equilibrium, $I_{\text{SS}}(u_0)$ (gray line, orange point), from $u_0=0.4$ to $u_1=1.4$. $d=0.5,V_T=0.5;I_s=1;a=1,b=1,{\tau }_k=0.01,R_s=0,C_m=0$.

Figure 10

Equivalent circuit of (a) current-controlled memristor and (b) a mixed-voltage and current-controlled memristor model. (c) Impedance spectrum with $C_m=0,R_b=3,R_a=-1,C_a=-10$.

Figure 11

(a) Current-voltage curves and (b) carrier density at constant voltage sweep of velocity, $v_s$. Parameters $\alpha =50,k=1,\beta =5,x_0=100$.

Figure 12

Memristor model of Eqs. (45)–(47) driven with a sinusoidal input of 1 V. (a) I-V curve, $R_{\text{on}}=50\mathrm{\Omega },R_{\text{off}}=1\mathrm{k}\mathrm{\Omega }$, and (b) state variable x. Reproduced with permission from Ref. [65]. Copyright 2013 IEEE.